Hertzian analysis of the nonlinear elastic response upon unloading provides analytical solutions that were used to verify if the hardness values measured on the super- and ultrahard coatings are self-consistent. The analytical solutions were also used to estimate the tensile strength of the coatings. The highest tensile stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of Gpa, thus giving an estimate of their tensile strength. The results show that the tensile strength of the superhard nanocomposites reaches an appreciable fraction of the ideal cohesive strength that is predicted on the basis of the universal binding energy relation. The data are compared with finite element computer modeling in order to, obtain a deeper insight into the complex problems. Reliable values of the hardness can be obtained if coatings of a thickness greater than 8 mum are used and the load-independent values are measured at sufficiently large indentation depths of greater than 0.3 mum. (C) 2003 American Vacuum Society.